Verified Answer :

MattD

The parallelogram angle alpha and beta form 180 degrees (angles on one basis).
\(\alpha+\beta=180\)
\(\beta=9\alpha\)
\(9\alpha+\alpha=180\)
\(10\alpha=180|:10\)
\(\alpha=18\)
\(\beta=180-18=162\)

AL2006

If you pick any two angles out of a parallelogram, either they're equal, or else they add up to 180 degrees.

Call the smaller angle 'A'.  Then the bigger one is '9A' .
Their sum is 180 degrees.

10A = 180

Divide each side by 10 :

A = 18

One angle is 18 degrees.
The other one is 9 x 18 = 162 degrees.

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